Artificial selection changes the distribution of phenotypic trajectories \({\bf x}_{t_0}^{t_f} \equiv ({\bf x}_{t_0},\dots ,{\bf x}_{t_f})\)  from \(P_0({\bf x}_{t_0}^{t_f}) \)  in the stationary state under natural selection to a configuration closer to the desired target \(P_{\bf u}({\bf x}_{t_0}^{t_f})\) . In analogy to thermodynamics, we can associate a free energy to these distributions, as \(F_0= \log P_0({\bf x}_{t_0}^{t_f})\)  and \(F_u=\log P_u({\bf x}_{t_0}^{t_f})\)  [1]}. The expected difference between the free energy of the two phenotypic configurations can be interpreted as the amount of work done by artificial selection, which corresponds to the Kullback-Leibler distance between the two distributions,
\(W_u \equiv \langle F_u \rangle -\langle F_0\rangle = \int \, P_u({\bf x}_{t_0}^{t_f} ) \log \left[ \frac{P_{\bf u}({\bf x}_{t_0}^{t_f} ) }{P_0({\bf x}_{t_0}^{t_f} )}\right] \equiv D_{KL} (P_{\bf u}({\bf x}_{t_0}^{t_f} )| | P_0({\bf x}_{t_0}^{t_f} ))\) 
